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Spin orientation in solid solution -ilmenite Erik Brok, Cathrine Frandsen, Kim Lefmann, Suzanne Mcenroe, Peter Robinson, Benjamin P. Burton, Thomas C. Hansen, Richard Harrison

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Erik Brok, Cathrine Frandsen, Kim Lefmann, Suzanne Mcenroe, Peter Robinson, et al.. Spin orien- tation in solid solution hematite-ilmenite. American Mineralogist, Mineralogical Society of America, 2017, 102 (6), pp.1234-1243. ￿10.2138/am-2017-5792CCBY￿. ￿hal-01691798￿

HAL Id: hal-01691798 https://hal.archives-ouvertes.fr/hal-01691798 Submitted on 24 Jan 2018

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. American Mineralogist, Volume 102, pages 1234–1243, 2017

Spin orientation in solid solution hematite-ilmenite k

Erik Brok1,2,3,4, Cathrine Frandsen1, Kim Lefmann5, Suzanne McEnroe6, Peter Robinson7, Benjamin P. Burton8, Thomas C. Hansen9, and Richard Harrison10,*

1Department of Physics, Technical University of Denmark, DK-2800, Kongens Lyngby, Denmark 2Center for Electron Nanoscopy, Technical University of Denmark, DK-2800, Kongens Lyngby, Denmark 3Center for Neutron Scattering, National Institute of Standards and Technology, MD-20899, Gaithersburg, Maryland, U.S.A. 4Department of Materials Science and Engineering, University of Maryland, MD-20742, College Park, Maryland, U.S.A. 5Nano-Science Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark 6Norwegian University of Science and Technology, N-7491, Trondheim, 7Geological Survey of Norway, N-7491 Trondheim, Norway 8Materials Measurement Laboratory, National Institute of Standards and Technology, MD-20899, Gaithersburg, Maryland, U.S.A. 9Institut Max von Laue Paul Langevin, F-38042 Grenoble 9, France 10Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.

Abstract The spin orientation in synthetic hematite-ilmenite samples and in a sample of natural hematite was studied from room temperature to above the antiferromagnetic-paramagnetic phase transition (the Néel

temperature; TN ≈ 600–950 K) by neutron powder diffraction and at room temperature by Mössbauer spectroscopy. The usually assumed magnetic structure of hematite within this temperature range is antiferromagnetic with the spins confined to the basal plane of the hexagonal structure; however, an out-of-plane spin component is allowed by the symmetry of the system and has been observed in recent studies of synthetic hematite samples. We find the spins in the antiferromagnetic sublattices to be rotated out of the basal plane by an angle between 11(2)° and 22.7(5)° in both synthetic hematite-ilmenite samples and in the natural hematite sample. The spin angle remains tilted out of the basal plane in the entire temperature range below the Néel temperature and does not depend systematically on Ti-content. The results indicate that the out-of-plane spin component is an intrinsic feature of hematite itself, with an origin not yet fully understood, but consistent with group theory. This represents a major shift in understanding of one of the two main systems responsible for rock magnetism. Keywords: Hematite, magnetic properties, spin orientation, neutron scattering, Mössbauer spectroscopy

Introduction is strong evidence that these properties are associated with fine scale exsolution structures observed in natural hematite-ilmenite The ilmenite-hematite [xFeTiO3 – (1 – x)Fe2O3] solid-solution series has been studied extensively because of its complex and samples (Robinson et al. 2002; Fabian et al. 2008; Brok et al. interesting magnetic and electronic properties. Intermediate 2014). Solid solution FeTiO3-Fe2O3 does not exhibit these well- compositions are magnetic semiconductors (Ishikawa and Aki- developed exsolution structures and can therefore be used as a moto 1957; Ishikawa 1958) and could conceivably be utilized baseline for determining if the observed properties are tied to in spintronics devices (Butler et al. 2003; Fujii et al. 2004). The the exsolution structure. Between the Néel temperature of TN ≈ 955 K (Morrish 1994) FeTiO3-Fe2O3 solid-solution series further serves as a model system for natural ilmenite-hematite , which are studied and the Morin temperature of TM ≈ 264 K (Besser et al. 1967; 3+ because of their remarkable magnetic properties and because of Morin 1950) hematite is a canted antiferromagnet with Fe their importance as a source of anomalies in the magnetic spins aligned ferromagnetically within the basal plane of the of the Earth (McEnroe et al. 2001; Kletetschka et al. 2002), and hexagonal structure while spins in adjacent planes are aligned possibly of other planets like Mars (McEnroe et al. 2004). Inter- antiferromagnetically apart from a small canting of about 0.065° esting magnetic properties of natural ilmeno-hematite samples that gives rise to a small net magnetization. The spin orientation is include giant exchange bias (McEnroe et al. 2007; Fabian et al. usually assumed to be in or very close to the basal plane (Morrish 2008) and large and stable remanent magnetization that cannot 1994; Shull et al. 1951; Flanders 1972) even though the sym- be explained by the individual properties of hematite and ilmenite metry of the structure allows for an out-of-plane spin component alone (McEnroe et al. 2002; Robinson et al. 2002, 2004). There (Dzyaloshinsky 1958). At TM hematite undergoes the so-called Morin transition in which the spins rotate 90° to form a perfectly antiferromagnetic structure (no canting) with spins in the two * E-mail: [email protected] sublattices parallel and antiparallel to the hexagonal [001] axis. k Open access: Article available to all readers online. The Morin transition is known to be suppressed by impurities as

0003-004X/17/0006–1234$05.00/DOI: http://dx.doi.org/10.2138/am-2017-5792CCBY 1234 BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE 1235

well as by finite crystallite size and the canted antiferromagnetic for Q1 ≠ 0, Q2 ≠ 0. The magnetic structure observed by experi- structure with spins close to the basal plane is maintained even at ment is the C2/c structure with Q1 ≠ 0 and Q2 = 0. This structure the lowest temperatures in nanoparticles smaller than 20 nm and is a canted antiferromagnet with parallel alignment of the spins in samples doped with even small amounts (<1%) of Ti (Bødker within each (001) layer and nearly antiparallel alignment of spins et al. 2000; Besser et al. 1967; Morrish 1994). in neighboring (001) layers (indices refer to the parent hexagonal

In a natural sample of ilmeno-hematite with nanoscale ex- unit cell). The primary order parameter Q1 places spins parallel solution lamellae of ilmenite in the parent hematite structure to the (001) basal plane and nearly perpendicular to the diad (i.e., Harrison et al. (2010) found the spins to be rotated 29.5° out nearly perpendicular to an a crystallographic axis of the parent of the basal plane and in a nanocomposite of hematite particles hexagonal unit cell). A degree of canting within the basal plane interacting with particles of NiO (Frandsen et al. 2011) measured is permitted by the C2/c symmetry, such that spins are rotated an out-of-plane angle as large as 70°. These experiments show by ~0.065° to create a weak ferromagnetic (WF) moment along that exchange interaction across interfaces can change the spin the diad (Morrish 1994). A secondary irreducible representation + + orientation in hematite. In studies of Al-substituted hematite (mG1) is permitted within C2/c. By itself, mG1 would give a it has been proposed that intermediate structures (spins not strictly antiferromagnetic alignment of spins normal to the (001) + parallel or perpendicular to [001]) exist close to the Morin transi- basal plane (as observed for T < TM). In combination with mG3, tion (Vandenberghe et al. 2001, 2002). Even in pure hematite at the antiferromagnetic spins are rotated about the diad so that ambient conditions out-of-plane spin-angles of about 18° have they lie at an angle, a, to the basal plane, as has been observed been measured by Parise et al. (2006) and Klotz et al. (2013). in recent experiments (Frandsen et al. 2011; Harrison et al. 2010;

The spin orientation in hematite between TM and TN is thus not Klotz et al. 2013; Parise et al. 2006). Note that even when a ≠ 0, always confined to the basal plane. The spin orientation could the canted WF moment still lies parallel to the diad and therefore depend on factors such as impurities and strain and could thus in the basal plane. If we assign a secondary order parameter Q3 + be sample dependent. In particular, the spin orientation in Ti- to mG1, then Q1 and Q3 are proportional to the in-plane and out- substituted hematite could deviate from that of pure hematite, of-plane spin components, respectively. Given the symmetry and may potentially vary with Ti-content. relationship between Q1 and Q3, it is permitted for these order The degree of Fe-Ti cation order in hematite-ilmenite solid parameters to couple bilinearly in the expansion of Gibb’s free solutions depends greatly on the composition and thermal history energy. In this case we would expect that Q3 would vary linearly of the sample. Quenched samples containing less than ~40% with Q1. This proposition can be tested directly by Rietveld ilmenite exhibit no long-range Fe-Ti cation order, and adopt refinement of high-temperature powder neutron diffraction data. the space group R3c. Quenched samples containing more than Here we follow the crystallographic conventions and refine- ~40% ilmenite exhibit an increasing degree of short- and then ment procedures described in detail by Harrison et al. (2010). For long-range Fe-Ti cation order with increasing ilmenite content, technical reasons, refinements were performed in a non-standard leading to a loss of symmetry from R3c to R3 (Harrison and A2/a setting of the monoclinic C2/c phase described above. For Redfern 2001). Quenched samples with intermediate compo- ease of comparison with the high-temperature hexagonal phase sitions are infamous for their ability to acquire self-reversed the unit-cell parameters are presented here using a monoclinic thermoremanent magnetization, linked to chemical and ordering pseudocell with volume equal to that of the high-temperature heterogeneities at the nanoscale (Fabian et al. 2011; Robinson hexagonal cell: am = (1/√3)[210]hex, bm = [010]hex, cm = [001]hex, et al. 2011, 2012, 2014). bm ~ 90°, where [abc]hex refers to the axes of the hexagonal

Here we investigate the spin-orientation in synthetic samples cell. Similarly the refined magnetic moments Mx and My in the of solid solution [xFeTiO3 – (1 – x)Fe2O3] with compositions x ≤ monoclinic cell are converted to components parallel (MP) and

0.40 and in a natural hematite sample (x = 0). We use Rietveld perpendicular (M^) to the basal plane. Figure 1 shows a represen- refinement of neutron powder diffraction data, taken at tempera- tation of the chemical and magnetic structure of hematite with a tures from room temperature to TN, to determine the average spin rotation of a = 20° away from the basal plane. out-of-plane spin angle a. We use Mössbauer spectroscopy to investigate the distribution of a in each sample. We find that the Methods spins in all hematite-ilmenite samples have significant out-of- Samples plane components in the range from a = 11(2)° to a = 22.7(5)°. Synthetic powder samples of [xFeTiO3 – (1 – x) Fe2O3] with nominal composi- All given uncertainties are the estimated standard deviations (s). tions of x = 0.13, 0.20, 0.35, and 0.40 were prepared by heating in sealed silica tubes

Even the natural hematite sample has a significant out-of-plane followed by rapid cooling of mixtures of Fe2O3 and TiO2 as described in Burton et al. spin-angle of a = 18.1(6)°. Our results show that a does not vary (2008). A natural sample of hematite was obtained from the Sedgwick Museum of systematically with Ti-content. Earth Sciences, Cambridge, U.K. The hematite sample was crushed and ground into a fine powder. We refer to these samples as ilm13, ilm20, ilm35, ilm40, and hem.

Group theory and crystallography Neutron powder diffraction

Magnetic ordering in hematite at temperatures TM < T < We performed neutron powder diffraction experiments at the OSIRIS instru-

TN can be described by a two-dimensional primary magnetic ment at the ISIS spallation neutron source, Oxfordshire, U.K., and at the D20 instrument at the reactor source at Institut Laue Langevin, Grenoble, France. In order parameter (Q1, Q2) corresponding to the active irreducible G+ both experiments the samples were mounted inside an evacuated furnace provid- representation (m 3) of the parent space group (R3c). Different ing a temperature range from room temperature to 1373 K (1100 °C). The Néel combinations of Q1 and Q2 to three possible magnetic space temperatures of the Ti-containing samples are expected to be lower (Besser et al. groups: C2/c for Q1 ≠ 0, Q2 = 0; C2ʹ/cʹ for Q1 = 0, Q2 ≠ 0; and P1 1967) than the 955 K of pure hematite, and the available temperature range should 1236 BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE

purity peaks were most pronounced. was refined as a both nuclear and magnetic phase in the R3m space group. Only a scale factor, the size of the magnetic moment, and unit-cell parameters were refined. The results from refinement of the magnetite structure are not expected to be very accurate or useful since this is just a minor impurity phase. For the other samples the magnetite content was so small that it was not necessary to include in the refinements.

When refining data from temperatures close to TN it was sometimes necessary to reduce the number of refined parameters, or to use Marquardt-damping to achieve convergence in the refinements. Refinement of the atomic occupation factors produced unrealistically small values compared to the nominal compositions. Instead an initial refinement of room-temperature diffraction data was performed for each sample using the nominal composition. The compositions (and thus the atomic occupation factors for Fe and Ti) were then determined from the refined unit-cell volume using the formula (Harrison et al. 2010)

V = 1.685 x2 + 10.823 x + 301.740 (x < 0.5) (1)

where V is the volume of the hexagonal unit cell in Å3. The occupancies were then fixed at the values obtained for the respective sample in each refinement. In the D20 experiment we measured a large number of diffraction patterns of

ilm13 above TN. This high-temperature data was refined to the high-symmetry hex- Figure 1. Crystal and magnetic structure between TM and TN. The agonal unit cell and with zero magnetic moment. At high temperatures (≈1100 K) large balls are O atoms and the smaller balls are Fe (or substituted Ti) we observed that diffraction lines from magnetite grew in intensity, probably be- atoms. The arrows indicate the spin orientation with a 20° tilt away cause of conversion of hematite to magnetite, and we therefore added a magnetite from the basal plane. phase in the refinements for the highest temperatures. Because of the conversion to magnetite the sample composition may change and the unit-cell parameters can therefore be expected to change at these high temperatures. thus allow us to obtain diffraction patterns from hundreds of degrees below, to The uncertainties given on parameters from the Rietveld refinements are the well above the magnetic phase transition. The samples were loaded in vanadium estimated standard deviations produced by GSAS or calculated from these using cylinders with thin walls to minimize contamination from the sample holder in standard error propagation methods. the diffraction patterns. We collected neutron diffraction patterns for the samples hem, ilm20, ilm35, Mössbauer spectroscopy and ilm40 at the OSIRIS instrument at ISIS. OSIRIS is a time-of-flight indirect 57Fe Mössbauer spectroscopy measurements at room temperature were per- geometry spectrometer/diffractometer with a ring of detectors for diffraction formed on samples hem, ilm20, ilm35, and ilm40. To prepare Mössbauer-absorber placed around the incident beam covering a range of scattering angles 150° < 2q samples a small amount of the sample was ground to a fine powder in an agate < 171°. The accessible d-spacing range is from 0.8 to 20 Å with optimal d-spacing mortar and ~30 mg of it was mixed with boron nitride and placed in a plastic holder. resolution Dd/d = 2.5 × 10–3. With choppers running at a 25 Hz frequency, a 4 Å The Mössbauer spectra were obtained at Department of Physics, Technical Univer- wide wavelength range with minimal contamination of higher order neutrons is sity of Denmark, Kgs. Lyngby, Denmark using a constant acceleration Mössbauer allowed to reach the sample. To obtain one diffraction pattern we perform four spectrometer with a source of 57Co in rhodium. The magnetically split spectra measurements with different relative phasings of the choppers to change the were fitted to sextets of Lorentzians with pairwise common line width of lines 1 incoming wavelength range and thus span the desired range of d-spacings. The and 6, 2 and 5, and 3 and 4. The area ratio between lines 1 to 6 was constrained to four measurements are combined to a diffraction pattern that continuously covers 3:2:1:1:2:3. The Mössbauer spectrometers were calibrated with a foil of a-Fe at d-spacings from approximately 0.72 to ~5.25 Å. room temperature and the isomer shifts are given relative to this calibration value. We obtained neutron diffraction patterns of the sample ilm13 at the high-flux powder diffractometer D20 at the ILL. The HOPG(002) monochromator with a take-off angle of 42° and the detector, covering 153.6° in 2q, provided us with Results neutrons of a wavelength of 2.4 Å and a d-spacing range of 1.3–13.1 Å with a Neutron powder diffraction resolution on the order of Dd/d = 10–2. While the resolution of D20 is inferior to that of OSIRIS, the high flux at The room-temperature diffraction patterns from the samples D20 enabled us to measure a diffraction pattern in a few minutes. It was therefore hem and ilm13 are shown in Figure 2. The positions of the (101) possible to measure a temperature series of closely spaced data points (in steps of and (003) magnetic peaks and the most intense of the peaks from about 5 K) from room temperature to far above the Néel temperature of the sample the magnetite impurity are indicated. The much better resolution (≈800 K) within one day. in the data from OSIRIS as compared to D20 is clearly seen by Rietveld refinements comparing the width of the peaks in the two diffraction patterns. The refined model represents the data reasonably well, and the To obtain the out-of-plane spin-angle a from the diffraction patterns taken below TN, Rietveld refinements were performed using the monoclinic model of disagreements between model and measurement originate pri- hematite in the space group A112/a, as described in Harrison et al. (2010), using marily from misfits of the peak profiles, which is a problem that the GSAS program (Larson and von Dreele 1994). The background was modeled can never be completely eliminated. There was some variation in with Chebyshev polynomials and the peak profile with appropriate peak shape background between samples and in some cases the background functions for time-of-flight (OSIRIS) and constant wavelength (D20) data. In all refinements the cations were assumed to be fully disordered. The validity of the was somewhat nonuniform and not that well modeled. However, assumption of cation disorder can be verified by the absence of reflections from it is important to note that for all samples the background was the R3 structure of FeTiO3 in the diffraction data. Long-range cation order would well modeled in the d-spacing range close to the two main mag- give rise to a nonzero intensity at the position of the magnetic hematite peaks netic peaks (101) and (003), which is the area of the diffraction above TN that was not observed. pattern that is most significant for obtaining information about For all samples, small peaks in the diffraction patterns were identified as belonging to the structure of magnetite. Because of this magnetite impurity, a the magnetic structure of the sample, in particular the out-of- magnetite phase was added to the refinements for ilm20 and hem where the im- plane spin-angle a. BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE 1237

A three-dimensional representation (d-spacing, temperature, dicating a reorientation of the spins close to TN. However, the intensity) of the complete set of measurements of the ilm13 relative uncertainties on the refined moments (especially M^) sample from room temperature (295 K) to above 1240 K is dis- become very large close to TN because the magnetic peaks are played in Figure 3. The magnetic phase transition is identified weak. The Néel temperatures determined from fitting the Mtot by the disappearance of the two main magnetic peaks [(101) at data to a power law d ≈ 4.2 Å and (003) at d ≈ 4.6 Å] at a temperature of ~800 K. β ⎛T −T ⎟⎞ = ⎜ N ⎟ The weak line at d ≈ 4.9 Å can be identified as a magnetic M M0 ⎜ ⎟ ⎝⎜ T ⎠⎟ reflection from magnetite and it completely disappears at the N Curie temperature of magnetite (≈ 850 K). Lines pertaining are given in Table 21. The fits represent the data well until very to the magnetite can also be identified (e.g., close to TN where the order parameter is expected to deviate at d ≈ 3.0 Å) and these achieve a significant gain in intensity from the power law because of critical behavior of the system. at temperatures around 1100 K, indicating that in addition to Because of the critical behavior a finite intensity remains in the a small initial impurity of magnetite part of the sample is be- magnetic peaks at temperatures a few K above the fitted TN. The ing reduced to magnetite during heating. When magnetite is critical exponent b determined from the fit to Mtot was in the produced by reduction of the sample the composition of the range 0.3–0.4 for all samples, which is in the expected range for remaining hematite-ilmenite becomes more Ti-rich resulting in a phase transition in a three-dimensional system. an enlargement of the unit cell seen as a shift of the diffraction In Figure 5 (left) the total moment is displayed as function lines to lower scattering angles (larger d-spacings). of the reduced temperature (T/TN) for all samples. In Figure 5 The refined unit-cell volumes and the determined composi- (right) the out-of-plane tilt angle a is displayed as a function of tions are given in Table 11 together with the room-temperature the reduced temperature. There is no systematic dependence values of the magnetic moments MP, M^, Mtot, and a. The com- of a on the Ti-concentration. The spin reorientation toward the positions deviate in some cases from the nominal values. In all basal plane with increasing temperature is systematic for all Ti- cases MP is significantly larger than M^, as expected for hematite containing samples with the exception of two points very close between TM and TN. However, there is a significant out-of-plane to TN (0.995 TN < T < TN) for the ilm35 sample. The figure also moment for all samples. The size of a varies from 11(2)° for illustrates that the uncertainty on a becomes large near TN. For ilm13 to 22.7(5)° for ilm35 and it does not depend systematically sample hem there is a significant change in a between the first on Ti-content. For the hem sample a = 18.1(6)°. and the second point, which are measured at room temperature

In Figure 4, we show MP, M^, and the total moment Mtot as and at 673 K (400 °C), respectively. function of temperature for the samples hem, ilm13, ilm20, and To illustrate the relationship between the primary order pa- ilm35. As the temperature increases toward TN both components rameter Q1 and the secondary order parameter Q3, M^ is plotted of the moment decrease at the same rate until close to TN. For against MP in Figure 6. For the hem sample the linear fit repre- the ilm13 and ilm20 samples M^ becomes zero before MP, in- sents the data well. For the ilm13 and ilm20 samples, M^ turns

to zero before MP ending the linear relationship between Q1 and

Q3 shortly before TN. For ilm35 the trend is the same as for the other Ti-containing samples if the three anomalous points closest

to TN are disregarded from the fit. In the experiment at D20 on sample ilm13 we obtained suffi-

cient data above and below TN to follow the transformation of the

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Figure 3. Representation of the set of diffraction patterns of ilm13 Figure 2. Room-temperature neutron powder diffraction patterns. measured at D20. The two lines at d ≈ 4.2 and d ≈ 4.6 Å are the hematite (a) Ilm13 measured at D20. (b) Hem measured at OSIRIS. The (101) and (003) magnetic peaks. The weak lines that gain in intensity at uncertainty (s) is smaller than the size of the points. temperatures above 1000 K are from the magnetite structure. 1238 BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE a b

c d

Figure 4. Refined in-plane (MP), out-of-plane (M^), and total (Mtot) moment as a function of temperature for samples hem, ilm13, ilm20, and ilm35. The solid lines are power law fits. The error bars represent one standard deviation s( ). a b

Figure 5. (a) Total magnetic moment as function of the reduced temperature. The solid lines are the same fits as in Figure 4. b( ) Out-of-plane tilt-angle a as function of the reduced temperature. The ilm13 data has been binned so that each data point represents a 17 K temperature interval. The error bars represent one standard deviation (s). monoclinic unit cell to the high-symmetry hexagonal cell oc- frame of the monoclinic pseudo-cell and can thus be compared curring simultaneously with the magnetic phase transition. The directly to the unit-cell parameters of the high-temperature change in the unit-cell parameters as a function of temperature can hexagonal cell, ah and ch. As the temperature increases am, bm be seen in Figure 7. The unit-cell parameters for the low-temper- converge toward the value of ah at TN. The slope of the curve ature monoclinic phase, am, bm, and cm are given in the reference does not change significantly at the phase transition, indicating BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE 1239 a b

c d

Figure 6. Out-of-plane vs. in-plane moment. The lines are linear fits to the blue data points. The error bars represent one standard deviation s( ). that the strain associated with the phase transition is small. The the fit. Here the uncertainties on the hyperfine parameters are same is true for the transformation of cm to ch. At high tempera- estimated from the uncertainties on the calibration with respect tures (above 1000 K) the slope of the ah and ch curves change. to a-Fe. The Lorentzian linewidths are 0.311, 0.288, and 0.249 This change happens in the same temperature range where the mm/s for lines 1 and 6, 2 and 5, and 3 and 4, respectively. Be- intensity of the magnetite lines start to increase (see Fig. 2) and cause the linewidths are close to the instrumental line width is probably associated with the reduction of some of the ilm13 to of 0.260 mm/s fitting with a more complicated model with a magnetite and the resulting change in hematite-ilmenite compo- distribution of hyperfine parameters is not justified. sition. The transformation of the crystallographic b-angle from The quadrupole shift (e) in the Mössbauer spectrum of monoclinic bm ≠ 90° to hexagonal bh = 90° can be followed in hematite is sensitive to a, and the fact that the spectrum is

Figure 8. At room-temperature bm is 90.039(7)°. As the tempera- well fitted with one symmetric sextet rather than two sextets 3+ ture increases bm decreases toward 90°. with different e indicates that the directions of the Fe spins Mössbauer spectroscopy in the sample are grouped around one value of a, rather than being distributed into distinct domains with different spin- The Mössbauer spectra of the hem, ilm20, ilm35, and ilm40 orientations. In particular, we can rule out a scenario with samples are shown in Figure 9. Also shown are model fits to the data. significant proportions of the spins being in the basal plane and Hematite sample. The spectrum of the hem sample consists along the c-axis, respectively. In principle the average value of a well-defined sextet as expected for pure hematite, as well of a can be found from the quadrupole shift of the spectrum as a small component (10% of the spectral area) that can be from (Morrish 1994) ascribed to the magnetite impurity, also observed in the neutron data. The room-temperature Mössbauer parameters of the he- 2 e = e0[3cos (90° – a) – 1]/2, (2) matite sextet are: Hyperfine field Bhf = 51.50(2) T, isomer shift

IS = 0.370(4) mm/s and quadrupole shift e = –0.094(4) mm/s where e0 depends on the quadrupole moment of the nucleus independent of whether the magnetite impurity is included in in the nuclear spin = 3/2 state, and on the electric field gradient 1240 BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE a b

Figure 7. Lattice parameters as function of temperature. The dashed vertical lines mark TN = 799.9 K. The data has been binned so that each data point represents a 17 K temperature interval. The uncertainty (s) is smaller than the size of the points.

are in the range between –0.110 and –0.076 mm/s. The ilm35 spectrum contains a central doublet with isomer shift 0.377(4) mm/s and quadrupole splitting 0.663(4) mm/s, suggesting that it could originate from a paramagnetic Fe3+ phase. The quadrupole shifts in the Ti-containing samples cannot be used to calculate a

from Equation 2 because e0 depends on the electric field gradient along the hexagonal c-axis, which is expected to change when Ti is substituted for Fe in the hematite structure. While it is not possible to calculate a the fact that the quadrupole shifts of all the Fe3+ sextets are close to –0.1 mm/s suggests that, like in the hem sample, the spin orientations are grouped around some aver- age angle, rather than two distinct populations of in-plane and out-of-plane spins. The room-temperature hyperfine parameters obtained from the sextet fits can be seen in Table 31.

Figure 8. The crystallographic bm angle as a function of temperature. Discussion The dashed vertical line marks TN = 799.9 K. The data has been binned so that each data point represents a 17 K temperature interval. The error The Rietveld refinement of the neutron powder diffraction bars represent one standard deviation (s). data tells us that there is a significant out-of-plane component of the hematite spins in all hematite-ilmenite samples and even along the c-axis. From the literature (Artman et al. 1968; Tobler in the natural hematite sample. While there is a variation in the et al. 1981) e0 can be estimated to e0 = 0.215(5) mm/s and a can measured a between samples it does not seem to depend sys- be determined from the measured quadrupole shift –0.094(4) tematically on Ti-content. There is no pronounced temperature mm/s to be a = 12(2)°. dependence of a, however, for the Ti-containing samples the

Mössbauer spectra of the hem sample were also collected at spins tend to reorient toward the basal plane close to TN, with the

80 and 20 K (not shown). These spectra taken below TM have exception of a few points very close to TN for ilm35. It should quadrupole shifts of 0.190(4) and 0.189(4) mm/s, respectively, be noted that very close to the phase transition the refinement corresponding to an imperfect Morin transition with the spins of the magnetic structure is susceptible to systematic errors and making an angle of 16(2)° with [001] even at 20 K. the parameters extracted from the refinements should not be Ti-containing samples. The room-temperature Mössbauer given too much weight. spectra of the samples ilm20, ilm35, and ilm40 have much From the quadrupole shift in the room-temperature Mössbau- broader lines than the hem spectrum. Each spectrum is fitted er spectrum of the hem sample the spin-angle can be determined with four sextets, three with isomer shifts close to 0.4 mm/s, cor- to a = 12(2)°, which is not consistent with the neutron result [a responding to Fe3+, and one with isomer shift closer to 0.6 mm/s, = 18.1(6)°], although it does confirm that there is a significant corresponding to Fe2+. The hyperfine fields of the Fe3+ sextets are out-of-plane component of the spin in the natural hematite in the range 47–50 T and thus a bit lower than expected for pure sample. The value of a determined from the quadrupole shift in hematite at room temperature (probably due to Ti4+ substitution the Mössbauer spectrum may not be taken as an accurate number 2+ in the hematite structure). The hyperfine field of the Fe sextet is because the hyperfine parameters (most importantly e0) may 37–44 T in all samples. The quadrupole shifts of the Fe3+ sextets depend delicately on crystallographic strain and other sample BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE 1241 dependent factors such as impurities in the structure. Because of purities are likely to be important for the macroscopic magnetic this uncertainty in the determination of a from Mössbauer spec- properties of the sample (the bulk magnetization) inclusions troscopy we regard the value obtained with neutron diffraction as of magnetite in the structure may not be important for the spin more accurate. From the Mössbauer spectrum taken at 20 K we structure in the hematite-ilmenite phase. Other impurities or find the spins to be rotated by 16(2)° from the c-axis. As soon as defects may, however, be important for the spin orientation and the spins are observed to be rotated away from the c-axis, a canted could explain the variation in spin angle between samples. moment becomes symmetry-allowed and could contribute to the It may seem surprising that we find a significant out-of-plane defect moment sometimes observed for hematite below TM. The spin component in hematite but it is consistent with the experi- spectrum also reveals that the spin orientation is not grouped in ments of Parise et al. (2006) and Klotz et al. (2013). While our distinct populations, e.g., one with a = 0° and one with a = 90° sample is a natural sample, which contains impurities that could corresponding to the spin orientation usually assumed above and affect its magnetic structure, the samples investigated by both below the Morin transition, but are grouped around some average Parise et al. (2006) and Klotz et al. (2013) were high-purity value. The Mössbauer spectra of ilm20, ilm35, and ilm40 suggest synthetic samples and impurities are thus unlikely to be the that this is the case also in Ti-substituted hematite. sole cause of the observations of out-of-plane spin orientation

We followed the structural phase transition at TN for a sample in hematite. Klotz et al. (2013) ascribe the spin orientation as (ilm13) with x = 0.176(12) and observed a gradual transition an artifact of the Rietveld method’s insensibility to changes in from the low symmetry monoclinic cell to the high symmetry a. It is true that the quality of the Rietveld-fit, as quantified by hexagonal cell. Within the resolution of D20 there is no strain the c2-value or any other measure of the sum of residuals, does associated with the phase transition. not depend strongly on the spin orientation but it is clear that The 30° out-of-plane spin-angle found by Harrison et al. the model with a = 20.0° (close to the refined value a = 18.1°) (2010) was believed to be linked to the exsolution microstructure represents the data much better than a = 0°, as can be seen in in the natural sample, and it is surprising that we find appreciable Figure 10, where the (101) and (003) magnetic peaks at room out-of-plane spin-angles in our samples that should not exhibit temperature are plotted together with models with different pronounced exsolution microstructure. While the neutron diffrac- values of a. However, the insensitivity of the fit to variations in tion data exclude a long-range ordering of the Ti-cations it is not a, when a is close to 0° has the consequence that the experiment possible to determine whether some short-range cation ordering becomes very susceptible to systematic errors. We have not exists. Frandsen et al. (2010) suggested that small clusters of identified any systematic errors in this experiment that could ordered hematite exist inside an ilmenite matrix for samples with give rise to the observed out-of-plane spin orientation. x > 0.5. They conclude that the size of the hematite clusters is The insensitivity to variations in the spin angle is not only on the order of 1–2 nm. Spins around the interfaces of such unique to the Rietveld method, but is a consequence of the clusters could be rotated due to exchange interaction between small change in 1–sin2(a) (which is essentially the measured Fe2+ and Fe3+ species. This would, however, not explain why we quantity) when a is small. To completely eliminate this prob- observe an out-of-plane spin orientation in the natural hematite lem one would have to perform a polarized neutron diffraction sample. The out-of-plane spin angle of 30° observed by Harrison et al. (2010) is significantly larger than the spin angles we find in our samples. This suggests that while some out-of-plane spin orientation may be intrinsic to the hematite magnetic structure exsolution could enhance the effect. It is well known that the magnetic structure of hematite does not prohibit an out-of-plane spin-component, however, it is generally assumed to be much smaller than the 18.1(6)° found in this work (Dzyaloshinsky 1958). The spin orientation in he- matite above and below the Morin transition is determined by a fine balance between competing anisotropies that may depend on factors such as impurities, strain, and applied pressure (Mor- rish et al. 1963; Artman et al. 1965; Besser et al. 1967; Klotz et al. 2013). In numerous neutron studies it has been observed that there is a finite intensity in the magnetic (003) reflection at temperatures far below the Morin transition (Morrish et al. 1963; Krén et al. 1974; Sváb and Krén 1979; Morrish 1994), proving that the spins are not perfectly aligned along the [001] axis below TM. Our results show that the spin alignment above Figure 9. Room-temperature Mössbauer spectra of hem, ilm20, the Morin transition can also be imperfect, with the spins rotated ilm35, and ilm40. The blue lines are the fits described in the text. The away from the (001) plane by a significant angle. hem data are fitted well with a single sextet for hematite plus two sextets All of the samples investigated in this work have impurities of for magnetite (black). The spectra of the Ti-containing samples are magnetite in amounts that give rise to visible diffraction peaks but fitted with four sextets (green) and for the ilm35 sample a small doublet that except for the hem sample are not detectible by Mössbauer component is added to the fit. The measurement uncertainty (s) is smaller spectroscopy due to overlapping lines. While the magnetite im- than the size of the points. 1242 BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE

work thus establishes a major shift in understanding of one of the two mineral systems responsible for rock magnetism.

Acknowledgments The neutron experiments were performed at ISIS, Oxfordshire, U.K. and Institut Max von Laue Paul Langevin, Grenoble, France. This work was supported by the Danish Agency for Science, Technology and Innovation through Dan Scatt. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007- 2013) ERC grant agreement 320750 and NERC Grant NE/D522203/1. The authors acknowledge the assistance of Aziz Daoud-Aladine during the experiments at ISIS. Figure 10. Refinement of the room-temperature hem data at a reduced d-spacing range 4.015–4.708 Å with different fixed values of References cited a. Only the magnitude of the magnetic moment and three background Artman, J.O., Murphy, C.J., and Foner, S. (1965) Magnetic anisotropy in antifer- parameters are refined and the remaining parameters are fixed at the values romagnetic -type sesquioxides. Physical Review, 138, 3A, A912. Artman, J.O., Muir, A.H., and Wiedersich, H. (1968) Determination of the nuclear from the refinement of room-temperature diffraction pattern in the entire 57m quadrupole moment of Fe from a-Fe2O3 data. Physical Review, 173, 337. experimental d-spacing range. The size of the refined magnetic moment Besser, P.J., Morrish, A.H., and Searle, C.W. (1967) Magnetocrystalline anisotropy does not deviate significantly from 4.21(2) mB when a is changed, except of pure and doped hematite. Physical Review, 153, 632–642. Bødker, F., Hansen, M.F., Koch, C.B., Lefmann, K., and Mørup, S. (2000) Magnetic when a = 30° where the total moment decreases to 4.01(3) mB. properties of hematite nanoparticles. Physical Review B, 61, 10, 6826–6838. Brok, E., Sales, M., Lefmann, K., Theil Kuhn, L., Schmidt, W.F., Roessli, B., experiment on a single crystal of hematite. Robinson, P., McEnroe, S.A., and Harrison, R.J. (2014) Experimental evidence for lamellar magnetism in hemo-ilmenite by polarized neutron scattering. We have studied the spin orientation in synthetic samples of Physical Review B., 89, 054430. hematite-ilmenite as well as a natural sample of hematite with Burton, B.P., Robinson, P., McEnroe, S.A., Fabian, K., and Boffa Ballaran, T. (2008) neutron powder diffraction and Mössbauer spectroscopy. We find A low-temperature phase diagram for ilmenite-rich compositions in the system Fe2O3-FeTiO3. American Mineralogist, 93, 1260–1272. that the spin has a significant component out of the basal plane Butler, W.H., Bandyopadhyat, A., and Srinivasan, R. (2003) Electronic and mag- in all samples. The nonzero tilt-angle of the antiferromagnetic netic structure of a 1000 K magnetic semiconductor: a-hematite (Ti). Journal of Applied Physics, 93, 7882. sublattices is consistent with other studies but we cannot at pres- Dzyaloshinsky, I. (1958) A Thermodynamic theory of “weak” ferromagnetism of ent give a detailed explanation of the origin of this deviation from antiferromagnetics. Journal of Physics and Chemistry of Solids, 4, 241–255. the usually assumed magnetic structure with the spins confined Fabian, K., McEnroe, S.A., Robinson, P., and Shcherbakov, V.P. (2008) Exchange bias identifies lamellar magnetism as the origin of the natural remanent mag- to the basal plane. The tilt angles in our samples are in the range netization in titanohematite with ilmenite exsolution from Modum, Norway. 11.0(9)–22.7(5)°, and seem not to depend systematically on Ti- Earth and Planetary Science Letters, 268, 339. Fabian, K., Miyajima, N., Robinson, P., McEnroe, S.A., Ballaran, T., and Burton, content. Furthermore, the out-of-plane angle does not require an B.P. (2011) Chemical and magnetic properties of rapidly cooled metastable exsolution structure as seen in natural samples. ferri-ilmenite solid solutions: implications for magnetic self-reversal and exchange bias, I. Fe-Ti order transition in quenched synthetic ilmenite 61. Implications Geophysical Journal International, 186, 997–1014. Flanders, P.J. (1972) Observation of a c-axis moment in a-Fe2O3. Journal of Ap- The implications of the present results can best be ap- plied Physics, 43, 2430–2435. preciated by reference to the theoretical paper on hematite Frandsen, C., Burton, B.P., Rasmussen, H.K., McEnroe, S.A., and Mørup, S. (2010) Magnetic clusters in ilmenite-hematite solid solutions. Physical Review magnetization by Dzyaloshinsky (1958), which showed both B, 81, 224423. the individual layer spin orientations and the spin-canted fer- Frandsen, C., Lefmann, K., Lebech, B., Bahl, C.R.H., Brok, E., Ancoña, S.N., romagnetic moments parallel to the (001) crystallographic Theil Kuhn, L., Keller, L., Kasama, T., Gontard, L.C., and Mørup, S. (2011) Spin reorientation in a-Fe2O3 induced by interparticle exchange interactions plane. This understanding persisted for the next half century in a-Fe2O3/NiO nanocomposites. Physical Review B, 84, 214435. and was enshrined in the major book Canted Antiferromagnet- Fujii, T., Kayano, M., Takada, Y., Nakanishi, M., and Takada, J. (2004) Ilmenite- hematite solid solution films for novel electronic devices. Solid State Ionics, ism by Morrish (1994). The first warnings that this might be 172, 289–292. incorrect came from Monte Carlo modeling of low-temperature Harrison, R.J., and Redfern, S.A.T. (2001) Short- and long-range ordering in the giant magnetic exchange bias in titanohematite with nanoscale ilmenite-hematite solid solution. Physical Chemistry of Minerals, 28, 399–412. Harrison, R.J., McEnroe, S.A., Robinson, P., Carter-Stiglitz, B., Palin, E.J., and ilmenite exsolution lamellae (Harrison et al. 2007), and evi- Kasama, T. (2007) Low-temperature exchange coupling between Fe2O3 dence that such exchange bias could be produced when similar and FeTiO3: Insight into the mechanism of giant exchange bias in a natural nanoscale intergrowth. Physical Review B, 76, 174436. natural samples were cooled in zero field to low temperature Harrison, R.J., McEnroe, S.A., Robinson, P., and Howard, C.J. (2010) Spin orienta- before the hysteresis experiment (Fabian et al. 2008). These tion in a natural Ti-bearing hematite: Evidence for an out-of-plane component. studies implied that an unexpected out-of-plane component of American Mineralogist, 95, 974. Ishikawa, Y. (1958) Electrical properties of FeTiO3-Fe2O3 solid solution series. spin should exist in the hematite, even at room temperature Journal of the Physical Society of Japan, 13, 37–42. and above. This was later observed directly in a similar ex- Ishikawa, Y., and Akimoto, S. (1957) Magnetic properties of the FeTiO3-Fe2O3 solved sample (Harrison et al. 2010), but was then attributed solid solution series. Journal of the Physical Society of Japan, 12, 1083–1098. 2+ Kletetschka, G., Wasilewski, P.J., and Taylor, P.T. (2002) The role of hematite- to a localized effect of Fe cations at interfaces. The present ilmenite solid solution in the production of magnetic anomalies in ground- and results indicate instead, for the first time, that the out-of-plane satellite-based data. Tectonophysics, 347, 167. spin component is an intrinsic feature of hematite itself, with Klotz, S., Strässle, Th., and Hansen, Th. (2013) Pressure dependence of Morin transition in a-Fe2O3 hematite. Europysics Letters, 104, 16001. an origin not yet fully understood, but consistent with group Krén, E., Molnàr, B., Svàb, E., and Zsoldos, E. (1974) Neutron diffraction study of theory. Probably earlier workers mistook the crystallographic the (1-x)Fe2O3-xAl2O3 system. Solid State Communications, 15, 1707–1710. Larson, A.C., and von Dreele, R.B. (1994) General Structure Analysis System position of the spin-canted ferromagnetic moment as also the (GSAS). Los Alamos National Laboratory Report LAUR 86-748. position of the individual layer spin components. The present McEnroe, S.A., Robinson, P., and Panish, P.T. (2001) Aeromagnetic anomalies, BROK ET AL.: SPIN ORIENTATION IN SOLID SOLUTION HEMATITE-ILMENITE 1243

magnetic petrology, and rock magnetism of hemo-ilmenite- and magnetite-rich Chemical changes during quench and annealing. Geopysical Journal Interna- cumulate rocks from the Sokndal region, South Rogaland, Norway. American tional, 188, 447–472. Mineralogist, 86, 1447. Robinson, P., Harrison, R.J., Fabian, K., and McEnroe, S.A. (2012) Chemical and McEnroe, S.A., Harrison, R.J., Robinson, P., and Langenhorst, F. (2002) Nanoscale magnetic properties of rapidly cooled metastable ferri-ilmenite solid solutions: haematite-ilmenite lamellae in massive ilmenite rock: An example of “lamellar Implications for magnetic self-reversal and exchange bias, III. Magnetic magnetism” with implications for planetary magnetic anomalies. Geophysical interactions in samples produced by Fe-Ti ordering. Geophysical Journal Journal International, 151, 890–912. International, 191, 1025–1047. McEnroe, S.A., Skilbrei, J.R., Robinson, P., Heidelbach, F., and Langenhorst, Robinson, P., McEnroe, S.A., Fabian, K., Harrison, R.J., Thomas, C.I., and Mukai, F. (2004) Magnetic anomalies, layered intrusions and Mars. Geophysical H. (2014) Chemical and magnetic properties of rapidly cooled metastable ferri- Research Letters, 31, L19601. ilmenite solid solutions—IV. The fine structure of self-reveres thermoremanent McEnroe, S.A., Carter-Stiglitz, B., Harrison, R.J., Robinson, P., Fabian, K., and magnetization. Geophysical Journal International, 196, 1375–1396. McCammon, C. (2007) Magnetic exchange bias of more than 1 Tesla in a Shull, C.G., Strauser, W.A., and Wollan, E. (1951) Neutron diffraction by para- natural mineral intergrowth. Nature Nanotechnology, 2, 631. magnetic and antiferromagnetic substances. Physical Review, 83, 333–345. Morin, F.J. (1950) Magnetic susceptibility of aFe2O3 and aFe2O3 with added Sváb, E., and Krén, E. (1979) Neutron diffraction study of substituted hematite. . Physical Review, 78, 819–820. Journal of Magnetism and Magnetic Materials, 14, 184–186. Morrish, A.H. (1994) Canted antiferromagnetism: Hematite. World Scientific, Tobler, L., Kündig, W., and Savić, I. (1981) Investigation of the Morin transition Singapore. in α-Fe2O3 by the Mössbauer effect. Hyperfine Interactions, 10, 1017–1022. Morrish, A.H., Johnston, G.B., and Curry, N.A. (1963) Magnetic transition in pure Vandenberghe, R.E., Van San, E., and De Grave, E. (2001) About the Morin tran- and Ga doped a-Fe2O3. Physics Letters, 7, 3, 177. sition in hematite in relation with particle size and substitution. Parise, J.B., Locke, D.R., Tulk, C.A., Swainson, I., and Cranswick, L. (2006) The Czechoslovak Journal of Physics, 51, 7, 663–675. effect of pressure on the Morin transition in hematite (alpha-Fe2O3). Physica ——— (2002) Evidence of intermediate magnetic states in non-stoichiometric B–Condensed Matter, 385, 391. hematite. In M.F. Thomas, J.M. Williams, and T.C. Gibb, Eds., Hyperfine Robinson, P., Harrison, R.J., McEnroe, S.A., and Hargreaves, R.B. (2002) Lamel- Interactions (C), p. 209–212. Springer. lar magnetism in the haematite-ilmenite series as an explanation for strong remanent magnetization. Nature, 418, 517. ——— (2004) Nature and origin of lamellar magnetism in the hematite-ilmenite series. American Mineralogist, 89, 725–747. Robinson, P., Harrison, R.J., Myajima, N., McEnroe, S.A., and Fabian, K. (2011) Manuscript received April 1, 2016 Chemical and magnetic properties of rapidly cooled metastable ferri-ilmenite Manuscript accepted December 16, 2016 solid solutions: implications for magnetic self-reversal and exchange bias, II. Manuscript handled by Sarah Brownlee